A373738 -id:A373738 - cp's OEIS frontend

A372192 a(n) = A010846(n) - A373738(n).

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 6, 0, 0, 1, 2, 1, 1, 0, 2, 1, 1, 0, 6, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 7, 0, 1, 1, 0, 1, 7, 0, 2, 1, 7, 0, 1, 0, 2, 0, 2, 1, 7, 0, 1, 0, 1, 0, 8, 1, 1, 2

Offset: 1

Michael De Vlieger, Aug 06 2024

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Log log scatterplot of a(n), n = 6..2^20, ignoring a(n) = 0, with a color code where red indicates omega(n) = 2, gold omega(n) = 3, lime green = omega(n) = 4, spring green = omega(n) = 5, and blue = omega(n) = 6, where omega = A001221.

Cf. A010846, A373738.

{0}~Join~Table[Count[Range[n], _?(Divisible[n, Times @@ FactorInteger[#][[All, 1]]] &)] - Floor[(1/PrimeNu[n]!)*Times @@ Map[Log[#, n] + 1 &, FactorInteger[n][[All, 1]]]], {n, 2, 120}]

A375011 a(n) = A373738(n) - A008479(n).

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 5, 1, 4, 3, 1, 1, 6, 1, 5, 3, 5, 1, 6, 1, 5, 1, 5, 1, 11, 1, 1, 4, 5, 3, 8, 1, 5, 4, 7, 1, 12, 1, 6, 5, 6, 1, 8, 1, 7, 4, 6, 1, 8, 3, 7, 4, 6, 1, 17, 1, 6, 5, 1, 3, 14, 1, 6, 4, 12, 1, 9, 1, 6, 6, 6, 3, 15, 1, 8, 1, 7, 1, 18, 3

Offset: 1

Michael De Vlieger, Aug 14 2024

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Log log scatterplot of a(n), n = 2..2^20, ignoring a(1) = 0, with a color code where red indicates omega(n) = 2, gold omega(n) = 3, lime green = omega(n) = 4, spring green = omega(n) = 5, and blue = omega(n) = 6, where omega = A001221.

Cf. A001221, A008479, A246655, A372192, A373738.

{0}~Join~Table[facs = FactorInteger[n][[All, 1]]; r = Times @@ facs;
  Floor[(1/PrimeNu[n]!)*Times @@ Map[Log[#, n] + 1 &, facs]] -
    Count[Range[n], _?(Times @@ FactorInteger[#][[All, 1]] == r &)], {n, 2, 120}]

a(1) = 0; a(k) = 1 for k in A246655.

cp's OEIS Frontend

A372192 a(n) = A010846(n) - A373738(n).

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